ELECTROMAGNETIC BALANCE. 233 



Suppose that two identical circular coils, like those of a tangent 

 galvanometer, are fixed at right angles to each other, with a common 

 vertical diameter, and suppose that a needle is suspended in the 

 centre. If the currents I and I' are passed separately in the two 

 coils, a position may be found for the system such that the needle 

 is in the meridian. If < is the angle which one of the coils makes 

 with the meridian, G and G' the constants of the two coils, the 

 equation of equilibrium of the needle is then 



, , _ \S 



From this we get 



GI 



, GT' 



If the galvanometer constants G and G' are equal by con- 

 struction, it follows that 



I 



= tan 9. 

 I 



855. ELECTROMAGNETIC BALANCE. A. Becquerel* was also the 

 first to conceive the idea of weighing the action of the current. Let 

 us suppose that a magnet, suspended vertically to the beam of a 

 balance, is kept in the axis of a coil through which a current passes. 

 There is attraction or repulsion, according to the direction of the 

 current ; from symmetry the action would be zero if the middle of 

 the magnet were in the centre of the coil, and it acquires a maximum 

 value when the middle of the magnet is at a certain point P of the 

 axis, beyond the coil. The beam is made horizontal by adding or 

 removing weights, so as to balance the action of the current on the 

 magnet. 



The coil should have the form of an elongated cylinder, and the 

 magnet itself should be tolerably long, for otherwise the force would 

 be very feeble. In the case of a repulsion, the equilibrium is stable 

 when the centre of the magnet is more distant" from the centre of the 

 coil than the point P, which corresponds to the maximum. It is also 

 stable in the case of attraction, if the centre of the magnet was at 

 the point P, or in the neighbourhood, for the action is then sensibly 

 constant, and the balance has of itself a stable equilibrium. This is 



* A. BECQUEREL. C0w/ter r;afc.r, Vol. v., p. 35. 1837. 



